Bonus Examples.
The final set of examples show how one can push the rules to their limits; these all constitute quantum predictions and remain to be discovered experimentally! This section is not examinable!
- Two (hypothetical) examples of cycloaddition with an even number of antarafacial components. The first is a π4a + π6a cycloaddition, again following a 4n+2 rule of aromaticity.
This is a π2a + π2a + π2a + π2a photochemical (4n, even antarafacial = hν) addition and was contrived by Woodward and Hoffmann themselves to illustrate the point. 
- A [1,5] migration of a methyl group can either go suprafacially with retention of configuration at the methyl (preserving a plane of symmetry) or antarafacially with inversion of configuration at the methyl (preserving an axis of symmetry). This last reaction corresponds to two antarafacial components. In such a small (six-membered) ring, the latter is calculated to be 23.4 kcal/mol (98 kJ/mol) higher in free energy than the suprafacial/retention
But increasing the ring size to ten, as in a [1,9] methyl shift is predicted to result in a double-Möbius [1,9] antara/inversion mode being 15.2 kcal/mol lower in free energy than the more conventional Hückel [1,9] supra/retention route! In reality, lower energy [1,5] shifts are likely to compete with both the [1,9] shifts. 
- A ten-electron [5,5] sigmatropic rearrangement with two antarafacial components (and following the 4n+2 rule) might be possible. Note the "figure-8, double S" shape.
- An example with four antarafacial components, two for methyl transfer with inversion, and two for antarafacial transfers across a chain. Its even possible to formulate reactions with six antarafacial components!.
The End (for real)
© Henry S. Rzepa, 1978-2014. Hide|show Toolbar.